The Browns, Bears and Jets expressed the most interest in 49ers free-agent safety Donte Whitner over the weekend, a source told The Chronicle.

The 49ers are “still pushing” to retain Whitner, 28, but it appears likely there will be a competitive market for his services when free agency begins at 1 p.m. Tuesday.

As a Cleveland native who attended Ohio State, Whitner could have particular interest in overtures from the Browns, who are “very serious” about signing him, the Cleveland Plain Dealer reported. The Browns could be preparing for the potential loss of safety T.J. Ward, 27, who earned his first Pro Bowl berth in 2013. Eleven teams have reportedly expressed interest in Ward since the NFL’s so-called “legal tampering period” began Saturday.

Over the weekend, agents were permitted to begin negotiations to potentially lure unrestricted free agents from their current employer, but contracts couldn’t be signed.

Whitner has spent the past three seasons with the 49ers and earned his first Pro Bowl berth in 2012. He is expected to receive a more lucrative contract than the three-year, $11.75 million deal he signed in 2011.

In July, Whitner publicly lobbied for a new contract in the form of an extension from the 49ers. In December, he acknowledged no progress had been made on a long-term deal, but expressed his desire to stick in San Francisco.

“I definitely want to be here,” Whitner said. “I think we have something special on this defense. Young guy like (rookie) Eric Reid, I like playing with him. I like this secondary and the rest of the guys. I like coming to work. So we’ll see what happens.”

If Whitner signs elsewhere, it will mark the second straight year the 49ers have lost a high-profile safety in free agency. Last year, Dashon Goldson signed a five-year, $41.25 million deal with the Buccaneers.

After Goldson’s exit, the 49ers signed Rams safety Craig Dahl and traded up to select Reid with the No. 18 pick in the draft. Reid, Dahl, C.J. Spillman and Bubba Ventrone, who is a strictly a special-teams player, are their only safeties under contract for 2014.